Question

The beginning share price for a security over a three-year period was $50. Subsequent year-end prices were $62, $58 and $64. The arithmetic average annual rate of return and the geometric average annual rate of return for this stock was
A. 9.30% and 8.58%, respectively.
B. 9.30% and 7.89%, respectively.
C. 9.30% and 7.03%, respectively.
D. 9.30% and 6.37%, respectively.

Answer 1

Answer:

Arithmetic average rate of return = 9.30 %

geometric average annual rate of return = 8.58%

correct option is A 9.30 % and  8.58%

Explanation:

given data

beginning share price = $50

time = 3 year

end year 1 prices =  $62

end year 2 prices = $58

end year 3 prices =  $64

to find out

arithmetic average annual rate of return and the geometric average annual rate of return

solution

we get here return for each period that is express as

Period 1 = $\frac{end\ year1}{beginning}$     ...........1

Period 1 = $\frac{62-50}{50}$

Period 1 = 24%

and

Period 2 = $\frac{end\ year2}{beginning1}$

Period 2 =  Period 1 = $\frac{58-62}{62}$

Period 2 =  -6.45%

and

Period 3 = $\frac{end\ year3}{beginning2}$

Period 3 = $\frac{64-58}{58}$

Period 3 = 10.34%

so  

here Arithmetic average rate of return will be

Arithmetic average rate of return =  (24% + -6.45% + 10.34%) ÷ 3

Arithmetic average rate of return = 9.30%

and  

geometric average annual rate of return will be here as

geometric average annual rate of return = $((1+r1) *(1+r2)*(1+r3))^{1/3}$ - 1     ................2

geometric average annual rate of return = $((1+0.24) +(1-0.0645)+(1+0.1034))^{1/3}$ - 1

geometric average annual rate of return = 8.58%